Most commonly, speaking in a foreign accent is taught with the aid of a dialect CD. If you do not have access to these resources, then research movies and television shows that have characters with strong Russian accents. Find clips featuring these characters and listen to them speak so you can pick up on natural speaking patterns and intonations that may be unapparent from written instructions.
There is no direct translation between Russian and English in regard to the "th" sound, so, many Russians compensate by making the voiced "th" sound (as in "this") into a "z" sound, making "this" into "zis." For unvoiced "th" sounds (such as in "booth"), a "s" sound is usually implemented, changing "booth" into "boos."
Russian native speakers typically have trouble with the "w" sound in English. That means most change the "w" sound into the "v" sound, changing words like "war" into "var" and "Wednesday" into "Vednesday."
There is little distinction in Russian between long and short vowels. The vowel sounds are typically the short vowel sounds (a as in "father," e as in "bet," i as in "lit," o as in "lock," and u as in "cut"). Long vowels will typically be flattened as much as possible and shortened to as close to these sounds as possible.
Russians may also have a hard time with the "j" sound in English as there is no Russian equivalent. Many will combine the "d" and "zh" sounds together to form a "j" sound. Typically, it is a bit too harsh for native speakers.